|M.Sc Student||Rubanenko Ariel|
|Subject||State Estimation Using Measurements with Uncertain Time-Tag|
|Department||Department of Aerospace Engineering||Supervisors||Professor Yaakov Oshman|
|Dr. Hector Rotstein|
This Thesis is concerned with the effect of measurements having uncertain time-tag on the estimation performance of a Kalman filter (KF). This uncertainty may arise from several sources, such as low quality analog lines, erroneous time-tag sent by low quality sensors or clock mismatch between two computer-aided systems which cause the measurement to “jump” randomly between measurement lags. In most cases, small measurement time delays are either neglected or the designer is unaware of them, therefore a classical KF algorithm is implemented. The effect of the uncertain time-tag on the estimation performance of the KF is investigated by true performance analysis (TPA), in which the true estimations error mean and covariance are compared to the corresponding statistical variables assumed by the KF. The TPA performed in this work shows that the true estimation error statistical moments can differ significantly from the statistical properties assumed by the KF. It is shown that the KF does not predict well the measurement mean and covariance, which renders the true innovations process dependent on the system's state. Thus, the innovations process becomes colored and biased, whereas the KF assumes that it is zero-mean and white. It is shown that, when the system is unstable or marginally stable, the true innovations covariance can exceed the KF assumed one by far. In stable systems the true estimation error still exceeds the KF assumed one, but is bounded, whereas in unstable or marginally stable systems the estimation error can become unbounded, thus rendering the estimate useless. A real world example of a phenomenon caused by disregarded random measurement delay in inertial navigation system (INS) during transfer alignment is chosen to demonstrate the applicability of the closed-form TPA formulae developed in this work. The example is taken from the literature, and demonstrates the severe effect that small, unknown measurement time delay can have on the performance of a real INS.